Optimal. Leaf size=82 \[ -\frac{a^6}{21 x^{21}}-\frac{6 a^5 b}{19 x^{19}}-\frac{15 a^4 b^2}{17 x^{17}}-\frac{4 a^3 b^3}{3 x^{15}}-\frac{15 a^2 b^4}{13 x^{13}}-\frac{6 a b^5}{11 x^{11}}-\frac{b^6}{9 x^9} \]
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Rubi [A] time = 0.0996926, antiderivative size = 82, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ -\frac{a^6}{21 x^{21}}-\frac{6 a^5 b}{19 x^{19}}-\frac{15 a^4 b^2}{17 x^{17}}-\frac{4 a^3 b^3}{3 x^{15}}-\frac{15 a^2 b^4}{13 x^{13}}-\frac{6 a b^5}{11 x^{11}}-\frac{b^6}{9 x^9} \]
Antiderivative was successfully verified.
[In] Int[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^22,x]
[Out]
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Rubi in Sympy [A] time = 23.0091, size = 82, normalized size = 1. \[ - \frac{a^{6}}{21 x^{21}} - \frac{6 a^{5} b}{19 x^{19}} - \frac{15 a^{4} b^{2}}{17 x^{17}} - \frac{4 a^{3} b^{3}}{3 x^{15}} - \frac{15 a^{2} b^{4}}{13 x^{13}} - \frac{6 a b^{5}}{11 x^{11}} - \frac{b^{6}}{9 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**22,x)
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Mathematica [A] time = 0.0158606, size = 82, normalized size = 1. \[ -\frac{a^6}{21 x^{21}}-\frac{6 a^5 b}{19 x^{19}}-\frac{15 a^4 b^2}{17 x^{17}}-\frac{4 a^3 b^3}{3 x^{15}}-\frac{15 a^2 b^4}{13 x^{13}}-\frac{6 a b^5}{11 x^{11}}-\frac{b^6}{9 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[(a^2 + 2*a*b*x^2 + b^2*x^4)^3/x^22,x]
[Out]
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Maple [A] time = 0.008, size = 69, normalized size = 0.8 \[ -{\frac{{a}^{6}}{21\,{x}^{21}}}-{\frac{6\,{a}^{5}b}{19\,{x}^{19}}}-{\frac{15\,{a}^{4}{b}^{2}}{17\,{x}^{17}}}-{\frac{4\,{a}^{3}{b}^{3}}{3\,{x}^{15}}}-{\frac{15\,{a}^{2}{b}^{4}}{13\,{x}^{13}}}-{\frac{6\,a{b}^{5}}{11\,{x}^{11}}}-{\frac{{b}^{6}}{9\,{x}^{9}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b^2*x^4+2*a*b*x^2+a^2)^3/x^22,x)
[Out]
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Maxima [A] time = 0.689781, size = 95, normalized size = 1.16 \[ -\frac{323323 \, b^{6} x^{12} + 1587222 \, a b^{5} x^{10} + 3357585 \, a^{2} b^{4} x^{8} + 3879876 \, a^{3} b^{3} x^{6} + 2567565 \, a^{4} b^{2} x^{4} + 918918 \, a^{5} b x^{2} + 138567 \, a^{6}}{2909907 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^3/x^22,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.251884, size = 95, normalized size = 1.16 \[ -\frac{323323 \, b^{6} x^{12} + 1587222 \, a b^{5} x^{10} + 3357585 \, a^{2} b^{4} x^{8} + 3879876 \, a^{3} b^{3} x^{6} + 2567565 \, a^{4} b^{2} x^{4} + 918918 \, a^{5} b x^{2} + 138567 \, a^{6}}{2909907 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^3/x^22,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.13562, size = 75, normalized size = 0.91 \[ - \frac{138567 a^{6} + 918918 a^{5} b x^{2} + 2567565 a^{4} b^{2} x^{4} + 3879876 a^{3} b^{3} x^{6} + 3357585 a^{2} b^{4} x^{8} + 1587222 a b^{5} x^{10} + 323323 b^{6} x^{12}}{2909907 x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b**2*x**4+2*a*b*x**2+a**2)**3/x**22,x)
[Out]
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GIAC/XCAS [A] time = 0.269936, size = 95, normalized size = 1.16 \[ -\frac{323323 \, b^{6} x^{12} + 1587222 \, a b^{5} x^{10} + 3357585 \, a^{2} b^{4} x^{8} + 3879876 \, a^{3} b^{3} x^{6} + 2567565 \, a^{4} b^{2} x^{4} + 918918 \, a^{5} b x^{2} + 138567 \, a^{6}}{2909907 \, x^{21}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)^3/x^22,x, algorithm="giac")
[Out]